What is the current through an ideal $P-N$ junction diode shown in the figure below? (in $mA$)

The molecular formula of diphenylmethane is $C_{13}H_{12}$. How many structural isomers are possible when one of the hydrogen atoms is replaced by a chlorine atom?

The isothermal Bulk modulus of an ideal gas at pressure $P$ is

If $x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x$ and $z=b x+a y$,then $a^2+b^2+c^2+2 a b c$ is equal to

Let $f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule,$\int_0^2 f(x) dx$ is equal to

$50 \, g$ of copper is heated to increase its temperature by $10 \, ^\circ C$. If the same quantity of heat is given to $10 \, g$ of water,the rise in its temperature is ........ $^\circ C$. (Specific heat of copper $= 420 \, J \, kg^{-1} \, ^\circ C^{-1}$,Specific heat of water $= 4200 \, J \, kg^{-1} \, ^\circ C^{-1}$)